Polynomial interpolation in R3

In this article, we exhibit a 12-dimensional subspace G of polynomials of three variables of degree 3 which interpolates at an arbitrary 4 points, i.e., for every four distinct points u1, u2, u3, u4 R3 and for every function ƒ C(R3), there exists a function g G such that g(uj) = ƒ (uj), for j = 1, 2, 3, 4.